Research On Brittleness Of Complex System Based On Entropy And Set Pair Theory

In this paper, according to the development of the present stage on research of complex system importance of research of complex system's brittleness is pointed out. In the process of introducing complex system, we give the concept of complex system and method of judgement. Secondly, Based on the research of complex system, brittleness as one of the basic characteristics has been presented and argued for the first time. We give the definition of the brittleness, the characteristic of the brittleness, and the structure of the brittle basic element, for further analysis of complex system's brittleness laid the theoretical foundation. And, brittle sameness, brittle opposite, brittle fluctuation and brittle link function is established in a brittle basic element. Meanwhile, according to set pair theory, concepts of brittle link entropy is defined. Moreover, non-cooperative game theory is applied to meet the need of the research on the brittleness of complex system, just because the different subsystems pursue individual profit, the whole interest of complex system has to see the loss. When the subsystems cannot obtain the negative entropy from the environment, the entropy will reach the critical point of collapse. Finally, under the environment of non-cooperative game dynamics, the brittle simulation model has been established. The results of simulation show that the collapse of complex is due to the entropy increase of subsystems in a brittle basic element and non-cooperative game dynamics, however, the effective means can make the system avoid collapsing.